I use A Child's Geography: Explore His Earth with my children. I haven't used the Hillyer book (or even looked at it). My understanding is that Ann Voskamp wrote her books in the style of Hillyer but more up to date. I do use Hillyer's A Child's History and Ann Voskamp has certainly kept up that chatty relationship with the reader, as if she was in the room herself talking to you (like Hillyer does).
My children have learned A LOT from A Child's Geography: Explore His Earth. They still talk about their walk through the atmosphere (even though it was months ago) and many other things, such as the jigsaw pieces of the continents, the warm stove our planet moves around etc. I've ordered book 2 for next year.
The book really isn't any hassle at all, you read a loud like you would any other book, get narrations/dictation done. I use the book two to three times a week and each chapter lasts us about three weeks (because of how I break it down). On the third week the children do the activities in the book - which really are so simple, such as plotting where a spillage of shoes turned up in the Pacific on a map (this explained how tides and gyres work). Last week we did an experiment to find out how the water cycle works (no biggie, it took about 10 mins to complete and the kids learned (and saw first hand) how ocean water evaporates and then comes back as fresh water).
I don't think you'll be disappointed with Voskamp's book(s) but, knowing how much we love Hillyer's A Child's History, I don't think you'd be disappointed with A Child's Geography by Hillyer either. You have to decide what is best for your families needs.
BTW - we love Holling C. Holling books - Paddle to the Sea is one we are also using next year!